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Updated: Jul 15, 2026
08:34
Contribution of the Na+/K+ Pump to Rhythmic Bursting, Explored with Modeling and Dynamic Clamp Analyses
Published on: May 9, 2021
Origin of bursting through homoclinic spike adding in a neuron model
Paul Channell1, Gennady Cymbalyuk, Andrey Shilnikov
1Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30303, USA.
Physical Review Letters
|May 16, 2007
Summary
Spike adding in bursting neurons is caused by shifts in potassium current kinetics. This leads to more spikes per burst, driven by homoclinic bifurcations in neural models.
Area of Science:
- Neuroscience
- Computational Neuroscience
- Mathematical Biology
Background:
- Bursting activity is a fundamental neuronal firing pattern.
- Understanding the mechanisms of spike adding in bursting is crucial for neuroscience.
- Leech heart interneurons exhibit complex bursting dynamics.
Purpose of the Study:
- To investigate the origin of spike adding in bursting activity.
- To analyze the role of slow potassium current kinetics in spike generation.
- To elucidate the underlying bifurcation mechanisms.
Main Methods:
- Utilized a reduced mathematical model of the leech heart interneuron.
- Analyzed the effect of shifting activation kinetics of the slow potassium current.
- Employed Poincaré return mappings to study homoclinic bifurcations.
Main Results:
- Shifting slow potassium current kinetics to depolarized potentials increased spike count within bursts.
- Homoclinic bifurcations of a saddle periodic orbit were identified as the cause.
- These bifurcations define the transition between tonic spiking and quiescent phases.
Conclusions:
- The study reveals homoclinic bifurcations as the mechanism for spike adding in leech interneuron bursting.
- Slow potassium current kinetics play a critical role in modulating spike frequency during bursting.
- The findings provide insights into the dynamical control of neuronal excitability.
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